Write the equation of each line using the given information.a. The points (-4,1) and (2,4) both lie on the lineb. m= -1 and the point (2,-1) lies on the linec. It has the same slope as y = 5 and passes through (1,1)d. m= -3 and it has a y-intercept of (0,8)

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8Solution:a. The points (-4,1) and (2,4) both lie on the lineThe general line equation on which (a, b) and (c, d) lies is:[tex]y-\mathrm{b}=\frac{d-b}{c-a}(x - a)[/tex]Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)Thus the required equation is:[tex]y-1=\frac{4-1}{2-(-4)}(x-(-4))[/tex]On solving we get,[tex]\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}[/tex]b.) m= -1 and the point (2, -1) lies on the line The equation of line in point slope form is y – b = m(x – a)  where m is slope and (a, b) is a point on itHere m = -1 and (a, b) = (2, -1)Thus the required equation is: y – (-1) = -1(x - 2)  y + 1 = -x + 2  y = -x + 2 -1  y = -x + 1 c. )It has the same slope as y = 5 and passes through (1, 1)our line has same slope with y = 5, then our equation would be y = k  and it passes through (x, y) = (1, 1) so, then by substitution 1 = k k =1  Then our equation will be y = k y = 1 d. ) m= -3 and it has a y-intercept of (0, 8)line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept. Then, our equation will be y = -3x + 8We took y- intercept = 8 as it is the value of y when x = 0